5. At a certain university data was gathered on a sample of students in an attem

Question

5. At a certain university data was gathered on a sample of students in an attempt to understand the relatiouship between high school GPA and GPA at the university. The high school GPAs in the sample ranged from 2.75 up to 4.0, and the university GPAs ranged from 2.2 up to 3.8. The data was linear with linear regression UGPA = (0.675)HSGPA + 1.097. (a) What umiversity GPA would you predict for a student who carned a 3.0 in high school? b) What university GPA would you predict for a student who earned a 2.0 in high school? (c) What university GPA would you predict for a student who earned a 4.1 in high school? (d) Which of the three predictions is more likely to be closer to the real university GPA of a student with the corresponding high school GPA?

Explanation / Answer

Given, linear regression is : UGPA = (0.675)HSGPA+1.097..............(i)

a) Given, HSGPA = 3.0

Now, From (i) we have, UGPA = (0.675)(3.0)+1.097

i.e., UGPA = 3.122

Therefore, the predicted university GPA for the student who earned a 3.0 in high school is 3.122

b) Given, HSGPA = 2.0

Now, From (i) we have, UGPA = (0.675)(2.0)+1.097

i.e., UGPA = 2.447

Therefore, the predicted university GPA for the student who earned a 2.0 in high school is 2.447

c) Given, HSGPA = 4.1

Now, From (i) we have, UGPA = (0.675)(4.1)+1.097

i.e., UGPA = 3.8645

Therefore, the predicted university GPA for the student who earned a 4.1 in high school is 3.8645

d) The student who earned a 3.0 in high school is more likely to be closer to the real university GPA.

Since, 3.8645 and 4.1 both are out of the range of given university GPA and high school GPA.

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